Qarabag have beaten Dundalk 3-0 in Azerbaijan to end the Lilywhites' Champions League dream.
Jaime Romero scored either side of an Ailton header to secure a 4-1 aggregate win for the hosts at Dalga Arena.
Dundalk will now enter the Europa League qualifiers, where they will face Slovan Bratislava, with the first leg taking place in Slovakia next week.
Qarabag's home record in European football is an impressive one, and Gurban Gurbanov dominated proceedings from the outset.
Vinny Perth made one change to the team which drew 1-1 in the first leg at Oriel Park, with Daniel Cleary coming in for the injured Robbie Benson.
Gary Rogers was forced into a brilliant save inside 30 seconds, tipping Mahir Emrell's shot around the post after he was played through by Filip Ozobic.
Rahil Mammadov headed the resulting corner over the crossbar as Qarabag piled early pressure on the Lilywhites.
Dundalk recovered from their early scares to win three successive corners at the other end, with Sean Hoare heading the third corner straight at Vagner.
Qarabag defender Michel struck the crossbar with a good header in the seventh minute, and the hosts took the lead five minutes later.
After being picked out by Abdellah Zoubir, Romero cut inside past Dane Massey and found the bottom corner with a low shot that Rogers got a hand to.
12: GOAL! QARABAG FK 1-0 Dundalk. Jaime Romero beats Gary Rogers at the near post to give the home side the lead. Agg 2-1 LIVE now on eir sport 1!#LOIinEurope pic.twitter.com/MWE0c8I9nE — eir Sport (@eirSport) July 31, 2019
Zoubir hit the side-netting with a shot from distance, and Cleary reacted quickly moments later to deny the influential midfielder another opportunity.
Qarabag continued to threaten, but Dundalk began to string some passes together as the half wore on without creating any meaningful chances.
Substitute Dani Quintana went close for the home side early in the second half, forcing Rogers to push his effort behind for a corner.
Rogers then bravely smothered the ball at Emrell's feet in the 52nd minute, with Cleary denying Zoubir from the rebound.
Ailton's header was tipped over the bar by Rogers on the hour mark as Qarabag looked to bury the tie.
Pat Hoban made Vagner work with a flick six minutes later from Sean Gannon's fine cross, but Dundalk rarely looked like grabbing that all-important away goal.
The Azerbaijaini champions doubled their lead 13 minutes from time when Ailton headed Maksim Medvedev's excellent cross past Rogers.
75: GOAL! QARABAG FK 2-0 Dundalk. Agg 3-1. Qarabag full-back Ailton heads home at the far post to extend the home side's lead. LIVE now on eir sport 1!#LOIinEurope pic.twitter.com/A4ZcoM7ZWH — eir Sport (@eirSport) July 31, 2019
Romero made it 3-0 in the 87th minute, his effort finding the back of the net via a deflection off Andy Boyle after more great work from Zoubir.
Qarabag saw out the final few minutes to deservedly seal a place in the next round.
86: GOAL! QARABAG FK 3-0 Dundalk. Jaime Romero nets his second goal of the night to wrap up the tie. Agg 4-1 LIVE now on eir sport 1!#LOIinEurope pic.twitter.com/wCUyEdVolB — eir Sport (@eirSport) July 31, 2019
The good news for Dundalk is that their European hopes are still alive. They will enter a play-off for the Europa League group stages if they can overcome Slovan Bratislava over two legs.